Abstract

In this paper we present the work on the latest developments of a grid free method for computing13; inviscid unsteady flow past multiple moving bodies. Least Squares Kinetic Upwind Method (LSKUM)13; [3, 4] is a kinetic theory based grid free scheme for solving the inviscid compressible Euler equations of13; gas dynamics. LSKUM has been extended to applications with moving nodes (LSKUM MN) [8]. Spatially13; higher order accuracy is achieved (in LSKUM as well as LSKUM MN) using the two step defect13; correction method. In case of LSKUM MN, it has been shown that defect correction step necessitates13; the recalculation of moving fluxes [8, 9] at not only all the immediate neighbouring nodes (secondary13; nodes) but also at the neighbouring points of the secondary nodes. This leads to considerable increase13; in computational time. In the present work we propose to use the Modified CIR splitting (MCIR)13; [10, 11] to obtain spatially higher order accuracy in LSKUM MN. MCIR splitting is a method to13; achieve spatially higher order accuracy without using the two step defect correction method. Apart13; form the implementation of MCIR splitting in LSKUM MN, we have also adopted the weighted least13; squares approach based on Eigenvector basis [6]. In this approach the least squares approximations13; for all the derivatives reduce to an equivalent 1-D form. For the unsteady calculations we have used13; the well known dual stepping procedure [12].13; The present method has been validated for the AGARD [1] CT5 standard test case. This is the13; case of unsteady transonic flow past an oscillating NACA0012 airfoil. In order to demonstrate the13; power of the method to handle multiple oscillating bodies, we compute flow past an oscillating pair13; of NACA0012 airfoils, one behind the other.